Pseudo-nitzschia spp. blooms are a recurrent problem in many coastal areas globally, imposing some significant threats to the health of humans, ecosystems and the economy. Monitoring programmes have been established, where feasible, to mitigate the impacts caused by Pseudo-nitzschia spp. and other harmful algae blooms. The detection of such blooms from satellite data could really provide timely information on emerging risks but the development of taxa-specific algorithms from available multispectral data is still challenged by coupled optical properties with other taxa and water constituents, availability of ground data and generalisation capabilities of algorithms. Here, we developed a new set of algorithms (PNOI) for the detection and monitoring of Pseudo-nitzschia spp. blooms over the Galician coast (NW Iberian Peninsula) from Sentinel-3 OLCI reflectances using a support vector machine (SVM). Our algorithm was trained and tested with reflectance data from 260 OLCI images and 4607 Pseudo-nitzschia spp. match up data points, of which 2171 were of high quality. The performance of the no bloom/bloom model in the independent test set was robust, showing values of 0.80, 0.72 and 0.79 for the area under the curve (AUC), sensitivity and specificity, respectively. Similar results were obtained by our below detection limit/presence model. We also present different model thresholds based on optimisation of true skill statistic (TSS) and F1-score. PNOI outperforms linear models, while its relationship with in situ chlorophyll-a concentrations is weak, demonstrating a poor correlation with the phytoplankton abundance. We showcase the importance of the PNOI algorithm and OLCI sensor for monitoring the bloom evolution between the weekly ground sampling and during periods of ground data absence, such as due to COVID-19.